REML Method Research Articles

Genetische Parameter für Merkmale der Eiproduktion geschätzt mit additiven und Dominanzmodellen bei Legehennen

Abstract. Title of the paper: Genetic evaluation of egg production traits based on additive and dominance models in laying hens The study was conducted to estimate additive and dominance variances for egg production traits of two commercial purebred lines (A & D) of laying hens using an animal model analysis. Breeding values estimated from a dominance model were compared to those from an additive model. In total, 8625 records of line A and 8968 records of line D from three generations were used in the analysis. Every record contained information on the number of eggs laid between 20 and 28 (EN1-2), 28 and 48 (EN3-7) and between 20 and 48 (EN1-7) weeks of age. Further average egg weight (EW), egg weight at 28 (EW1), 33 (EW2) and 40 (EW3) weeks of age were available. An additive animal model and one- and three-trait dominance models including the inbreeding coefficients as covariates were fitted to the data. Simultaneous estimates of the additive and dominance variance components were obtained using the REML method. The estimates of h2 from the dominance models for EN1-2, EN3-7, EN1-7 and EW were 0.40, 0.15, 0.28 and 0.62 for line A and 0.38, 0.16, 0.26 and 0.53 for line D. The ratios d2 of the dominance variance to total variance were moderate for EN (0.12–0.13) and low for EW (0.04–0.07) within line A but relatively low for EN (0.03–0.12) and high for EW (0.12–0.21) within line D. Between the breeding values of the best 100 hens of each generation estimated with the additive and the dominance models for EN1-2, EN3-7, EN1-7 and EW high rank correlations (0.946, 0.896, 0.945 and 0.991 in line A and 0.996, 0.899, 0.971 and 0.951 in line D were found

Evaluation and interpretation of results for three cross-over designs

In cross-over designs, individual sequences of treatments are applied to the animals. Within such designs it is possible that every treatment could modify the effect of the subsequent treatment applied to the same animal. We compared three cross-over designs each with three treatments, three periods, and two blocks. This comparison was done with respect to the variance of the estimations of the effects and its biases caused by the interactions between the treatment and the carry over effect of the foregoing treatment. Moreover, different methods of estimating variance components and calculating the degrees of freedom were compared by means of simulation. If the animal variance component is small, then the bias of the REML estimator of the variance components is greater than one of the widespread ANOVA-estimator called 'TYPE3'. But nevertheless, the mean squared error of this estimation is smaller in the case of REML in comparison to ANOVA. Therefore, the REML method should be preferred. For calculating the degrees of freedom, the Kenward-Roger method should be used. After applying this method, the true significance level is almost equal to its required value, but if the Satterthwaite method is used, the true significance level will be too high. If the interaction (treatment × carry over) is ignored in the model although it exists, the standard error of the treatment effect estimation is too great, and, therefore, the true significance level is too small. The methods which have been evaluated are available in the SAS-procedure MIXED (<citeref rid="b9">SAS Institute, 1999a</citeref>). To assist the investigation of cross-over designs by using this software, we developed programs for data management and data analysis. These programs are available from the first author.

Genetic parameters for egg production and egg weight of laying hens housed in single and group cages

Abstract. The present study was conducted to estimate the heritability and genetic correlation of monthly egg production and egg weight of 2 lines White Leghorn hens in single and group cages. A total of 2289 records (line A) and 2596 records (line D) from single cages, 518 and 541 records (for line A and D, respectively) from group cages, were analysed. (Co) variance components of single cage data were analysed using the programme VCE4 applying the REML method and a multiple trait animal model. An EM-algorithm was used to obtain (co) variance components for group cage data. Genetic correlations between single and group cages were analysed using the programme VCE4 based on sire model. Heritability estimates for monthly egg production in single cages ranged from 0.08 to 0.44 (line A); 0.04 to 0.43 (line D) and those for group cages were 0.02 to 0.42 (line A); 0.02 to 0.19 (line D). Egg weight was highly heritable for single and group cages (heritability = 0.25 to 0.54). The genetic correlations between monthly and cumulative egg production were 0.25 to 0.95 (line A); 0.26 to 0.86 (line D) for single cage and 0.24 to 0.84 (line A); 0.26 to 0.96 (line D) for group cage. Cumulative egg production in single cage were highly correlated with those of group cages (0.89 and 0.63, respectively for line A and line D). Single cage records gave higher estimates of genetic parameter than group records. However, the trend of estimates is almost the same. High genetic correlations were found between single- and group cages in most of the production periods.

Multitrait and repeatability estimates of random effects on litter size in sheep

AbstractFive data sets with records of first, second and third lambings of the White Alpine sheep (WAS1, WAS2), the Brown-Headed Meat sheep (BFS), the Black-Brown Mountain sheep (SBS) and the Valais Black-Nose sheep (SNS) of Switzerland were used to estimate phenotypic and genetic parameters for litter size using a multitrait and a repeatability model by the REML method. The sets contained litter information from 26 274, 25 165, 18 913, 14 953 and 21 726 ewes, respectively. Average numbers of litters per ewe were between 2·09 and 2·31. Average litter sizes at birth were between 1·36 and 1·57 lambs in first, between 1·52 and 1·75 in second and, between 1·56 and 1·86 in third parities. Multitrait estimates of heritability for size of first litters were 0·164, 0·157, 0·117, 0·223 and 0·116 for the WAS1, WAS2, BFS, SBS and SNS data, respectively. The corresponding estimates were 0·176, 0·165, 0·140, 0·208 and 0·134 for second and, 0·141, 0·155, 0·121, 0·145 and 0·107 for third litters. The systematic increase in phenotypic variances from first to third litter within data sets favoured the multivariate over the repeatability approach. Genetic correlations between size of the first three litters were, with one exception, above 0·927. Random flock ✕ year and sire of litter effects contributed between 2·2% and 13·2% and between 0·7% and 4·7% to the phenotypic variance of the traits, respectively. Residuals contributed between 70·6% and 84·2% to this parameter, estimates for the third litter were always highest. Heritability estimates from the repeatability model were smaller than the smallest multivariate estimates. Expected genetic gain in litter size from selection on the multitrait model was equal to the achieved response from the repeatability approach.

Developmental Instability and Sexual Selection in Stag Beetles from Chernobyl and a Control Area

Radioactivity may have both phenotypic and genetic effects through its disruption of physiological processes and mutations. I studied the size and asymmetry of secondary sexual and ordinary morphological characters of stag beetles (Lucanus cervus) in two areas in the Ukraine: near Chernobyl, where levels of radiation are high, and in a control area with low background radiation. Developmental instability of morphological characters was estimated from the degree of fluctuating asymmetry using the restricted maximum likelihood parameter estimation (REML) method to partition measurement error from asymmetry. The degree of asymmetry estimated from unsigned differences in size of right and left secondary sexual character was similar to estimates based on the REML method. Beetles from the contaminated area had a significantly elevated level of fluctuating asymmetry in the secondary sexual character compared with animals from the control area. Male stag beetles found with a female had significantly lower asymmetry than males found alone. While mated males did not differ in asymmetry between areas, unmated males from Chernobyl were much more asymmetric than unmated males from the control area. These findings provide evidence for radiation disrupting developmental homeostasis, and thereby affecting the mating status of free‐living beetles.

Estimation of additive and non‐additive genetic parameters for reproduction, growth and survival traits in crosses between the Moroccan D’man and Timahdite sheep breeds

Genetic breed differences, heterosis, recombination loss, and heritability for reproduction traits, lamb survival and growth traits to 90 days of age were estimated from crossing D’man and Timahdite Moroccan breeds. The crossbreeding parameters were fitted as covariates in the model of analysis. The REML method was used to estimate (co)variance components using an animal model. The first estimation of crossbreeding effects for Timahdite and D’man breeds shows that breed differences in litter traits are mainly of maternal genetic origin: +1.04 lambs, +1.88 kg, +0.60 lambs, and +2.23 kg in favour of D’man breed for litter size at lambing, litter weight at lambing, litter size at weaning, and litter weight at 90 days, respectively. The breed differences in lamb growth and survival are also of maternal genetic origin for the majority of traits studied, but in favour of the Timahdite breed: +3.48 kg, +45 g day−1 and +0.19 lambs for weight at 90 days, for average daily gain between 30 and 90 days of age, and for lamb survival to 90 days, respectively. The D’man direct genetic effect was low and negative for survival and birth weight of lambs during the first month of life. All traits studied showed positive heterosis effects. Recombination loss effects were not significant. Therefore, crossbreeding of Timahdite with D’man breeds of sheep can result in an improved efficiency of production of saleable lambs. Heritability estimates were medium for litter size but low for the other reproduction traits. Direct heritabilities were low for body weights and lamb survival at 90 days and the corresponding maternal heritabilities showed, however, low to moderate estimates. For litter traits, the estimates of genetic and phenotypic correlations were positive and particularly high for genetic correlations.

Exact and approximate REML for heteroscedastic regression

Exact REML for heteroscedastic linear models is compared with a number of approximate REML methods which have been proposed in the literature, especially with the methods proposed by Lee and Nelder (LN98) and Smyth and Verbyla (SV99) for simultaneous mean-dispersion modelling in generalized linear models. It is shown that neither of the LN98 or SV99 methods reduces to REML in the normal linear case. Asymptotic variances and efficiencies are obtained for these and other estimators of the same general form. A new algorithm is suggested, similar to one suggested by Huele et al., which returns the correct REML estimators and an improved approximation to the standard errors. It is possible to obtain REML estimators by alternating between two generalized linear models but the final fitted generalized linear model objects will not return the correct standard errors for the variance coefficients. The true REML likelihood calculations therefore fit only partially into the double generalized linear model framework.

Selection for ultrafine Merino sheep in New Zealand: heritability, phenotypic and genetic correlations of live weight, fleece weight and wool characteristics in yearlings

AbstractMerino yearling records from 1988 to 1992 birth years in ultrafine wool selection and random control flocks at Tara Hills High Country Station, New Zealand were analysed for live weight, fleece weight and wool characteristics. Estimates of heritability, genetic and phenotypic correlations among traits using REML methods are presented. Heritabilities (h2) of birth, weaning, autumn, spring and summer live weights and greasy and clean fleece weights were estimated as being 0·35, 0·34, 0·44, 0·43, 0·49, 0·24 and 0·28 respectively; while h2 of yield, fibre diameter, coefficient of variation in fibre diameter, staple crimp, staple length, staple strength, position of break, resistance to compression, bulk, CIE Y and CIE Y-Z were estimated to be 0·58, 0·59, 0·60, 0·45, 0·71, 0·13, 0·18, 0·46, 0·38, 0·38 and 0·42 respectively. Genetic correlations were found to be high among the live weights but low to moderate among fleece weight and wool characteristics. Heritability estimates of fibre diameter, fibre diameter variation and staple length were found to be higher in New Zealand fine wool Merinos than most of those reported in the literature. The results indicate that selection for reduced fibre diameter will have little effect on other major production traits such as live weight and fleece weight.

Estimated genetic parameters for growth traits of German shepherd dog and Labrador retriever dog guides.

A desirable dog guide weighs 18 to 32 kg and measures 53 to 64 cm in height at the withers as an adult. Heritabilities and genetic correlations were estimated for birth weight, 42-d weight, mature weight, and mature height for 2,334 German shepherd dogs and 2,028 Labrador retrievers raised by the Seeing Eye, Inc., Morristown, NJ, from 1979 to 1997. Data included 5,006 observations for German shepherd dogs from 113 dams and 33 sires and 4,123 observations for Labrador retrievers from 89 dams and 29 sires. A mixed effects model was considered with sex and birth year as fixed effects. Random effects were animal, maternal, and litter incorporating all pedigree information available. A derivative-free REML method was used to estimate parameters. The maternal component was higher than the additive genetic component for birth weight. Heritability of mature weight was estimated as 0.57 +/- 0.07 for German shepherd dogs and 0.44 +/- 0.07 for Labrador retrievers. Mature height heritability was estimated as 0.35 +/- 0.08 for German shepherd dogs and 0.46 +/- 0.08 for Labrador retrievers. Selection for lighter dogs at maturity is predicted to decrease the average mature height, and selection for taller dogs at maturity is predicted to increase the average mature weight. The estimated genetic parameters will aid in the development of strategies to increase the probability of breeding dogs for optimum mature size.

Genetic and environmental influences on size of first litter in sheep, estimated by the REML method

Fixed effects of age at first litter and of season of lambing as well as variance components for additive genetic, flock × year and sire of litter effects on size of first litter were estimated for an animal model by a derivative‐free REML procedure. Data of the four Swiss sheep breeds White Alpine (WAS), Brown‐headed Meat (BFS), Black‐Brown Mountain (SBS) and Valais Black Nose (SN) were available. Number of first litters used were 21 384, 21 607, 15 013, 12 394 and 18 110 the WAS (two data sets, WAS1, WAS2), BFS, SBS and SN, respectively. Litter size of ewes lambing the first time at 2 years of age was 0.27, 0.31, 0.41, 0.46 and 0.26 lambs larger than of ewes lambing the first time at 1 year of age. The largest increase occurred for the two breeds (BFS, SBS) with the lowest average age at first litter. The largest difference between any two lambing seasons within breed were 0.16, 0.16, 0.29, 0.22 and 0.07 lambs. Estimates of additive genetic variance of size of first litter were between 0.0269 (SN) and 0.0765 (SBS). Heritability estimates for this trait were 0.171, 0.156, 0.114, 0.225 and 0.122 for WAS1, WAS2, BFS, SBS and SN, respectively. A large flock × year component (relative to phenotypic variance) of 0.148 was found for SN, compared with estimates between 0.042 and 0.067 for the other breeds. A sire of litter component (relative to phenotypic variance) of 0.066 was found for SN, compared with estimates between 0.016 and 0.039 for the other breeds. It can be concluded that all nongenetic effects investigated should be taken into account for the estimation of additive genetic variance and breeding values for size of first litter, and that considerable variation in size of genetic and nongenetic effects exists in the sheep breeds under consideration.

Estimação de parâmetros genéticos de medidas de conformação, produção de leite e idade ao primeiro parto em vacas da raça Gir Leiteiro

RESUMO - Foram utilizados 573 registros zootécnicos de vacas primíparas da raça Gir Leiteiro para estimar os componentes de (co)variância das características de conformação, produção de leite em até 305 dias de lactação (PLEI) e idade ao primeiro parto (IPP) pelo Método da Máxima Verossimilhança Restrita (REML). Esses componentes foram utilizados no cálculo dos coeficientes de herdabilidade e nas correlações genéticas, fenotípicas e residuais. As medidas de conformação, circunferência torácica (CTOR), altura na garupa (AG), comprimento corporal (CC), comprimento de tetas (CT), diâmetro de tetas (DT) e altura de úbere (AU) foram realizadas em vacas à primeira lactação, com idade média de 4,05 anos. As correlações genéticas e fenotípicas entre PLEI e IPP foram 0,49 e 0,18, respectivamente. As correlações genéticas entre as características foram: PLEI x CTOR = -0,37; PLEI x AG = -0,62; PLEI x CC = -0,52; PLEI x CT = -0,08; PLEI x DT = -0,12; PLEI x AU = -0,69; IPP x CTOR = -0,05; IPP x AG = -0,37; e IPP x CC = 0,25. As estimativas de correlações genéticas entre produção de leite e medidas de tamanho corporal, de modo geral, indicam que a seleção para produção de leite teria, como resposta correlacionada, diminuição do tamanho da vaca.

The bootstrap procedure in individual bioequivalence.

A bootstrap-type hypothesis test procedure for assessing individual (or population) bioequivalence between two drug formulations is suggested in a draft guidance from the United States Food and Drug Administration (FDA). The purpose of this article is to study the unknown properties of this test procedure and propose some improved test procedures. We find that: the FDA's bootstrap computation is not correct; the power of the FDA's test can be very low; the use of the REML method suggested in the draft guidance does not have any advantage over the use of simpler methods such as the moment method; and the method of sample size determination in the draft guidance is inappropriate. We study the size and power of different bootstrap test procedures and suggest a method for sample size determination. It is our hope that this article will draw some attention to further research in this area, and eventually a satisfactory statistical method can be implemented for assessing individual (or population) bioequivalence.

Genetic analysis of velvet antler yield in farmed elk (Cervus elaphus)

Data from the Alberta Agriculture Food and Rural Development data base, which keeps inventories of elk producers and velvet production information (n = 12 724), were used to estimate genetic and phenotypic variances, heritability and repeatability estimates for velvet antler using REML methods. The heritability based on the animal models I and II was 0.27 ± 0.03 and the repeatability ranged from 0.31 ± 0.02 to 0.35 ± 0.03 depending on the animal model used. Antler yield is expected to respond to selection as the heritability is medium, but non-additive and environmental effects can also influence production. Key words: Elk, heritability, repeatability, antler production

Adjusted likelihood methods for modelling dispersion in generalized linear models

This paper considers double generalized linear models, which allow the mean and dispersion to be modelled simultaneously in a generalized linear model context. Estimation of the dispersion parameters is based on a χ 2 1 approximation to the unit deviances, and the accuracy of the saddle-point approximation which underlies this is discussed. Approximate REML methods are developed for estimation of the dispersion. The approximate REML methods can be implemented with very little added complication in a generalized linear model setting by adjusting the working vector and working weights. S-Plus functions for double generalized linear models are described. Through two data examples it is shown that the approximate REML methods are more robust than maximum likelihood, in the sense of being less sensitive to perturbations in the mean model. Copyright © 1999 John Wiley & Sons, Ltd.

Efeito do ajustamento para os períodos de serviço anterior e corrente sobre os valores genéticos de touros para produção de leite na raça Holandesa

Os períodos de serviço anterior e corrente foram considerados, simultaneamente, como efeitos fixos em um modelo de touro para produção de leite até 305 dias (L305), contendo ainda os efeitos fixos rebanho-ano-estação e grau de sangue, idade da vaca como covariável (até 3º grau) e os efeitos aleatórios de touro e vaca. Foi usada uma matriz de parentesco que incluiu o touro, seu pai e sua mãe. O mesmo modelo, excluindo-se idade da vaca, foi usado para produção de leite até 305 dias ajustada para idade à maturidade (PROAJU). O método da máxima verossimilhança restrita (REML) foi usado para resolução das equações por meio do programa MTDFREML. Pelas soluções, concluiu-se que a PROAJU aumentou 902 kg, quando o período de serviço anterior variou de 20 a 300 dias. Este aumento foi de 813 kg para a mesma variação no período de serviço corrente. Os valores genéticos dos touros para PROAJU foram obtidos em quatro conjuntos de dados, usando-se o mesmo modelo anterior com exclusão dos períodos de serviço anterior e corrente. Os registros de produção foram ajustados com os fatores multiplicativos obtidos para período de serviço anterior e corrente e os touros foram reavaliados. Correlações de ordem entre valores genéticos dos touros para produção de leite ajustada e não-ajustada foram próximas de 1. As médias das diferenças entre valores genéticos dos touros com as produções de leite ajustadas e não-ajustadas para os períodos de serviço foram aproximadamente zero, indicando que os fatores para período de serviço foram adequados para os dados.

Diferenças genéticas e estimação de coeficientes de herdabilidade para características morfológicas em fêmeas zebus e F1 holandês x zebu

O objetivo deste trabalho foi averiguar possíveis variações nas mensurações morfológicas entre reprodutrizes zebus dos grupos genéticos (GG) Indubrasil, Nelore e Tabapuã e entre os GG de suas filhas F1 Holandês x Indubrasil (HxI), Holandês x Nelore (HxN) e Holandês x Tabapuã (HxT), além de estimar coeficientes de herdabilidade (h²) para estas características. O método dos quadrados mínimos foi usado para verificação das diferenças nas características morfológicas entre os GG e para obtenção de estimativas de h² pela regressão filha-mãe (RFM). O método REML foi também usado para estimar h². Os dados foram coletados em 183 vacas zebus e 273 novilhas F1 Holandês x Zebu. O GG das fêmeas F1 foi importante para sua inscrição no livro de controle e registro genealógico da raça Girolando, pois os GG obtiveram diferentes pontuações nas características de classificação total para tipo, aparência geral e caracterização leiteira. Para estas três características, as mestiças HxI obtiveram melhor pontuação que as HxN e as novilhas HxT, pontuação intermediária. Entre as características morfológicas, as larguras entre as tuberosidades ilíacas e as isquiáticas, o comprimento da garupa, a profundidade torácica, a altura na cernelha e o peso corporal não apresentaram diferenças entre os três GG zebus e entre suas progênies F1 Holandês x Zebu. As estimativas de herdabilidade variaram de 0,09 (profundidade torácica) a 0,59 (comprimento da orelha) pela RFM e de 0,09 a 0,89 (mesmas características) pelo método REML. Os resultados indicam que, em sistema de cruzamento com a raça Holandesa, para a produção de novilhas F1 para venda, o GG Indubrasil produziu animais melhor caracterizados, como da raça Girolando, os quais, possivelmente, teriam maior apelo comercial que os dos GG Tabapuã e Nelore. Adicionalmente, as estimativas de herdabilidade indicaram que a seleção para características morfológicas levaria a ganhos genéticos diretos razoáveis.

Quantitative genetics of reproductive traits in the edible snailHelix aspersa Müller

The present study was carried out to obtain accurate estimates of genetic parameters for the following reproductive traits in Helix aspersa: interval between end of hibernation and mating (R1), interval between mating and egg- laying (R2), and for each clutch, egg number and mean egg weight. Genetic correlations with growth traits were also estimated. Data from 983 (1780 for R1) animals issued from 123 full-sib families were analyzed. Genetic parameters were estimated with REML method applied to an animal model. Observation of egg number and R1 revealed that some early adult animals (snails with reflected peristome) were not entirely sexually mature. Heritabilities were low or medium: 0.12 ± 0.01 for egg number; 0.37 ± 0.01 for mean egg weight; 0.21 ± 0.01 for R1, and 0.15 ± 0.01 for R2. Genetic correlations were favourable to selection for improving adult weight because egg number and mean egg weight were positively correlated with adult weight. J. Exp. Zool. 281:220–227, 1998. © 1998 Wiley-Liss, Inc.

Genetic parameters for traits other than production in purebred and crossbred New Zealand dairy cattle

Abstract First lactation classification records for 17 non-production traits in New Zealand dairy cows, and survival from first to second and to third lactation were analyzed in order to estimate the correlations amongst the 17 traits and with cow survival. Four of the traits were farmer-scored, 13 were scored by inspectors. The data were collected on heifers calving between 1987 and 1991, to allow expression of survival through to 3rd lactation. Analyses were carried out by breed of sire (of cow), for Holstein, Ayrshire and Jersey sires and combined, with breed and heterosis effects included. Approximately 20% of the cows were crossbred, mainly combinations of Jersey and Holstein. The 17 traits were scored on a 1 to 9 scale; a Snell transformation of the scores was used for the analyses using mixed model REML methods. The overall rate of survival to 2nd lactation was 0.88 and to 3rd lactation was 0.74. The genetic correlations between the producer-scored traits and survival to 2nd and to 3rd lactations were mainly in the range 0.3 to 0.6 whereas the genetic correlations between the inspector-scored, ‘conformation’ traits were not different from zero. Heritabilities for the producer-scored traits ranged from 0.1 to 0.37, for the inspector-scored traits heritabilities ranged from 0.076 to 0.45.

Estimation of genetic parameters for test-day milk production at different stages of lactation of Finnish Ayrshire heifers

Genetic parameters for test-day milk production at different stages of lactation of Finnish Ayrshire heifers were estimated with the REML method using the AI algorithm and animal model. The data consisted of 38 679 first lactation test-day milk yields of 4205 cows from 231 herds in three geographical regions (North Savo, Central Ostrobothnia and Lapland). To identify different test days, records were numbered according to the days in milk after calving, and were further categorized into three part-lactations according to the test-day classification. Expressions in the three part-lactations were considered as separate traits, and tests were treated as repeated observations within the trait. Heritability estimates for test-day milk yield varied between 0.11 and 0.17, being lowest at the beginning of lactation. Genetic correlations between test-day milk yields at different trimesters ranged from 0.64 to 0.91, being highest between consecutive trimesters. Standard errors of the estimates of genetic parameters varied between 0.02 and 0.08. Genetic interrelationships differed from 1.0, supporting the assumption that genetic variation exists in the shape of the lactation curve. The necessity of considering deviations from the general lactation curve in the test-day model, e.g. fitting random regression coefficients, is discussed.

Maximum Likelihood Estimation of Genetic Parameters in Life-History Studies Using the `Animal Model'

1. Restricted maximum likelihood using the «Animal Model» (REML) and least squares (LS) analyses of a quantitative genetic study of life-history traits are compared. The REML method is considered generally superior although the advantages are not great if the data analysed come from nearly balanced one-generation designs. 2. Although in the analysis of several traits multivariate analysis is desirable it did not prove practicable because of its computational demands